Overlap Spectrum Fiber Bragg Grating Sensor Based on Light ... - MDPI

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Overlap Spectrum Fiber Bragg Grating Sensor Based on Light Power Demodulation Hao Zhang 1, *,† , Junzhen Jiang 2,† , Shuang Liu 1 , Huaixi Chen 3 , Xiaoqian Zheng 1 and Yishen Qiu 2 1 2 3

* †

Department of Electronic Information Science, Fujian Jiangxia University, Fuzhou 350007, China; [email protected] (S.L.); [email protected] (X.Z.) Fujian Provincial Key Laboratory for Photonics Technology, Fujian Normal University, Fuzhou 350007, China; [email protected] (J.J.); [email protected] (Y.Q.) Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, China; [email protected] Correspondence: [email protected] or [email protected] The authors contributed equally to this work.





Received: 19 April 2018; Accepted: 15 May 2018; Published: 17 May 2018

Abstract: Demodulation is a bottleneck for applications involving fiber Bragg gratings (FBGs). An overlap spectrum FBG sensor based on a light power demodulation method is presented in this paper. The demodulation method uses two chirp FBGs (cFBGs) of which the reflection spectra partially overlap each other. The light power variation of the overlap spectrum can be linked to changes in the measurand, and the sensor function can be realized via this relationship. A temperature experiment showed that the relationship between the overlap power spectrum of the FBG sensor and temperature had good linearity and agreed with the theoretical analysis. Keywords: fiber Bragg grating; demodulation; overlap spectrum; temperature sensors

1. Introduction Fiber Bragg gratings (FBGs) are key passive optical components with numerous advantages including an all-fiber geometry, small size, low insertion loss, good insulation, and high flexibility [1]. As a result, they have attracted considerable attention because of their wide range of applications in fiber sensors, fiber filters, fiber lasers, dispersion compensators, and other optoelectronic devices [2–5]. Fiber sensors based on FBGs have high sensitivity and resolution and facilitate measurements via changes in reflection spectrum or transmitted spectrum induced by the measured entities [6]. FBGs are widely used to measure temperature, stress, humidity, and many other physical quantities [7–10]. One of the key issues associated with FBGs sensors that is actively under investigation is signal demodulation. Traditional demodulation methods make use of an optical spectrum analyzer (OSA) [1]. The advantages of this method include a simplified construction and extremely high resolution. However, the OSA is extremely expensive and inconvenient to perform. Thus, this approach is impractical for real-world application. Alternative methods based on well-known optical instruments and tools, such as Fabry-Perot filters, the Mach–Zehnder interferometer, and linear edge filters have been investigated for FBG demodulation to reduce the difficulty and the cost of applications of FBG [11–14]. However, these methods are limited to some extent by a range of factors including low sensitivity, limited ability to easily adjust the measurement range, high complexity, and the utilization of devices that are not readily available [15]. A novel overlap spectrum FBG sensor based on light power demodulation is presented in this paper. It uses two chirp FBGs (cFBGs) of which the reflection spectra partially overlap each other to

Sensors 2018, 18, 1597; doi:10.3390/s18051597

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realize sensor function. The light power of the overlap spectrum can be associated with changes in a measurand. The has atosimple structure and a low temperature measurement experiment experiment wasdesign designed test the performance ofcost. the A FBG sensor. The experimental results was designed to test the performance theoutput FBG sensor. The experimental that the revealed that the relationship betweenofthe light power of the FBG results sensor revealed and temperature relationship the output power of the range FBG sensor andestimated temperature good could exhibitbetween good linearity, and light the measurement could be and could easily exhibit controlled. linearity, and the measurement range could be estimated and easily controlled. 2. Configuration and Principles 2. Configuration and Principles The two configurations of the overlap spectrum FBG sensor based on light power The two configurations overlap FBG is sensor based onoflight power demodulation demodulation are shown of in the Figure 1. spectrum The system comprised a broadband-amplified are shown in Figure 1. The system comprised of a broadband-amplified spontaneous-emission (ASE) spontaneous-emission (ASE) lightissource, a three-port or four-port circulator, two cFBGs, and an light source, a three-port or four-port circulator, two cFBGs, and an optical power meter (OPM). The optical power meter (OPM). The reflection spectra of the two cFBGs must partially overlap each reflection of the light two cFBGs each other. Thetobroadband light signal other. Thespectra broadband signalmust frompartially the ASEoverlap light source couples cFBG A via port 2 offrom the the ASE light source couples to cFBG of A light via port of the circulator. cFBG A reflects a portion of light circulator. cFBG A reflects a portion that2 matches the Bragg reflection condition to cFBG B that matches the Bragg reflection condition to cFBG B via port 3 of the circulator. cFBG B reflects via port 3 of the circulator. cFBG B reflects a portion of light with wavelengths in the overlapa portion ofband light of with in the spectrum of the two cFBGs, remaining spectrum thewavelengths two cFBGs, and theoverlap remaining light isband transmitted light. The and OPMthe is connected light is transmitted light. The OPM isthe connected to light port 4from of the circulator to receive the reflected to port 4 of the circulator to receive reflected cFBG B for the configuration usinglight the from cFBG B for the configuration using the four-port circulator. The OPM is connected to cFBG B to four-port circulator. The OPM is connected to cFBG B to receive the transmitted light from cFBG B receive the transmitted lighta from cFBG circulator. B for the configuration using a three-port circulator. for the configuration using three-port

Figure 1. Configuration of an overlap spectrum fiber Bragg gratings (FBG) sensor based on light Figure 1. Configuration of an overlap spectrum fiber Bragg gratings (FBG) sensor based on light power power demodulation, (a) using a four-port circulator, and (b) using a three-port circulator. demodulation, (a) using a four-port circulator, and (b) using a three-port circulator.

cFBG A works as a broadband filter in the design and cFBG B is a sensitive element or sensor A worksreflection as a broadband filter in the cFBG B iswhen a sensitive element or sensor head.cFBG The overlap spectrum of the twodesign cFBGsand is invariable they are not affected by head. The overlap reflection spectrum of the two cFBGs is invariable when they are not affected environmental change. However, the overlap spectrum will change when one of the cFBGs is by environmental change. However, the overlap spectrum when one of the cFBGs externally perturbed. Therefore, the overlap spectrum can be will usedchange to monitor any measurand that is is externally perturbed. Therefore, the overlap spectrum can be used to monitor any measurand that is capable of influencing the shift of reflection spectrum of cFBG B. capable influencing the shift of spectrum of cFBG B. Theofrelationships between thereflection reflection spectra and transmission spectra of cFBGs A and B are The relationships between the reflection spectra and transmission spectra of cFBGs A and B are shown in Figure 2. For simplicity, the following discussion is based on the wavelength-shift of cFBG shown in Figure 2. For simplicity, the following discussion is based on the wavelength-shift of cFBG B B in the long wave direction, and the contrary is the case when the wavelength of cFBG B shifts to in the long wave direction, and the contrary is the case the wavelength the the short wave direction. For strong Bragg gratings, thewhen reflected light power of of cFBG cFBGsBAshifts and to B can be considered to be concentrated in the range of the full-width-at-half maximum (FWHM) bandwidth, and the reflection spectrum can be treated approximately as a rectangular distribution.

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The FWHM bandwidths of the reflection spectra of cFBGs A and B are BA and BB, respectively, and 3 of 11 the edge wavelengths of the reflection spectra of the cFBGs are as follows,

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B



A short wave direction. For strong Bragggratings, light power of cFBGs A and B can be  reflected  RA  DA the 2 considered to be concentrated in the range of the full-width-at-half maximum (FWHM) bandwidth, (1)  B and the reflection spectrum can be treated as a rectangular distribution. The FWHM A  approximately FA  DA  bandwidths of the reflection spectra  of cFBGs A and 2 B are BA and BB , respectively, and the edge wavelengths of the reflection spectra of the cFBGs are as follows,

B (  B BA RBλRADB = λ DA2 − 2  λ = λ + BA BB 2  FA DA FB DB  ( 2 , BB

(2)

(1)

λ RB = λ DB − 2 , (2) λ FB = λ DB +ofB2Bthe reflection spectra of cFBGs A and B, where λRA and λRB are the rising-edge wavelengths respectively; λFA and λFB are the falling-edge wavelengths; and λDA and λDB are the center where λRA and λRB are the rising-edge wavelengths of the reflection spectra of cFBGs A and wavelengths of cFBGs A and B, respectively. Obviously, the reflection spectrum received by the B, respectively; λFA and λFB are the falling-edge wavelengths; and λDA and λDB are the center OPM in Figure 1a is the overlap between cFBGs A and B. The bandwidth of the overlap spectrum is wavelengths of cFBGs A and B, respectively. Obviously, the reflection spectrum received by the given by: OPM in Figure 1a is the overlap between cFBGs A and B. The bandwidth of the overlap spectrum is given by:  BA    BB      FA   RB    DA  2 BA   DB  2  BB  DA   DB  λ FA −  λ RB = λ DA +   − λ DB − λ DA < λ DB 2 2 BR   (3)    BA  BR = (3) B BB    BA λ B   DA   λ FB − FBRA  = RA  λ DB DB +   DA λ   DB > λ DB − λ −   DA DA 2 2  



2  

2 

Figure 2. Relationships between the reflection spectra and transmission spectra of the sensor when Figure 2. Relationships between the reflection spectra and transmission spectra of the sensor when the the wavelength of cFBG B shifts in the long wave direction (a) for λDA < λDB, and (b) for λDA < λDB. wavelength of cFBG B shifts in the long wave direction (a) for λDA < λDB , and (b) for λDA < λDB .

Figure 2 shows that the transmitted spectrum from the cFBG B is related to the reflection FigureAs 2 shows that the transmitted spectrum from the cFBG B is Therefore, related to the spectrum. spectrum. one increases, and the other decreases necessarily. thereflection transmitted light As one increases, and the other decreases necessarily. Therefore, the transmitted light received by the received by the OPM in Figure 1b can also be used to measure the measurand. In theory, the two OPM in Figureshown 1b canin also be used to measure measurand. In theory, the two configurations shown configurations Figure 1 have the samethe effect. Furthermore, the bandwidth of transmitted light in Figure 1 have the same effect. Furthermore, the bandwidth of transmitted light from the cFBG B in from the cFBG B in Figure 1b is: Figure 1b is:       BBBB  BA  B   λ RB − RBRA  = RA  λ DB DB −    −  DA λ DA − 2A  DA λ  DB < λ DB DA 2 λ   2    2   BT = . (4) BT  −  λ  λ FB = λ DA + B A − λ DB + BB (4) λ DA > λ DB FA 2 BA 2 BB  FA   FB    DA   2  

       DB   2   

 DA   DB

.

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The reflected light power for the configuration using a four-port circulator can be deduced as: PR =

Z BR

P(λ)dλ ≈

BR a PI , BI 1

(5)

where BI is the FWHM bandwidth of input light from the ASE source; PI is the total power of the input light; and a1 is attenuation of the system, which is mainly caused by the circulator (port 1 to port 2, port 2 to port 3, and port 3 to port 4). Similarly, the transmitted light power for the configuration using a 3-port circulator is: Z B (6) PT = P(λ)dλ ≈ T a2 PI , BI BT where a2 is the attenuation caused by the circulator (port 1 to port 2, and port 2 to port 3). The Bragg wavelength-shift occurs when cFBG B, which is utilized as a sensitive element, is influenced by a measurand such as temperature, stress, humidity, and so on. The reflected light power and the transmitted light power vary with the Bragg wavelength-shift. The sensitivity coefficient of the wavelength-shift of cFBG B with the measurand is η, and the varied reflected and transmitted light power is: ( B ±η∆x PR + ∆PR = R BI a1 PI , (7) B ∓η∆x PT + ∆PT = T BI a2 PI where ∆x is the variation of the measurand. Obviously, the variation of the light power received by the OPM is proportional to ∆x, and we have: (

∆PR = ∆PT =

±ηa1 PI B I ∆x ∓ηa2 PI B I ∆x

= κ∆x , = κ∆x

(8)

where κ is the sensitivity coefficient of the overlap spectrum FBG sensor. Figure 3 shows that the light power received by the OPM varies with the wavelength-shift of cFBG B. The wavelength-shift conditions of the upper limit and lower limit of the reflected power and transmitted power are shown in Table 1. The maximum spectrum range that can be used for measurements is deduced from Figure 3 and Table 1. It is expressed as: ( B B B A > BB η Rmax = . (9) BA B A < BB η Equation (9) shows that the measurement range can be controlled by choosing the FWHM and the sensitivity coefficient η of the cFBGs.

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Figure 3. The maximum spectrum range that can be used for measurements when the wavelength of

Figure 3. The maximum spectrum range that can be used for measurements when the wavelength of cFBG B shifts to the long wave direction (a) for λDA < λDB and BA > BB, (b) for λDA < λDB and BA < BB, (c) cFBG B shifts to the long wave direction (a) for λDA < λDB and BA > BB , (b) for λDA < λDB and BA < BB , for λDA > λDB and BA > BB, and (d) for λDA > λDB and BA < BB. (c) for λDA > λDB and BA > BB , and (d) for λDA > λDB and BA < BB . Table 1. Wavelength-shift condition of the upper limit and lower limit of the reflected power.

Table 1. Wavelength-shift condition of the upper limit and lower limit of the reflected power.

Center FWHM Wavelength Condition DB BA > BB Light Power Center Wavelength λDA < λFWHM Condition Upper limit (reflected)/lower limit λDA < λDB BA < BB (transmitted) λDA > λDB BA > BB BA > BB λDA < λDB Upper limit λDA > λDB BA < BB BA < BB λDA < λDB (reflected)/lower limit λDA < λDB BA > BB BA > BB λDA > λDB (transmitted) Lower limit (reflected)/upper λlimit λDA < λDB BA < BB BA < BB DA > λDB (reflected) λDA > λDB BA > BB λDA < λDB BA > BB BA < BB λDA > λDB Lower limit Light Power

λ < λDB B < BB (reflected)/upper limit Note: FWHMDA denotes the full-width-at-half A maximum bandwidth. λDA > λDB BA > BB (reflected) λ > λDB BA < BB 3. Experiments and Discussion DA

Wavelength-Shift Condition Wavelength-Shift λFB = λFA Condition λRB = λRA λRB= =λλFA RA λFB FA λRBλFB = =λλRA FA λRBλRB = =λλ RA λ RB = λ λFB = λFAFA λFB = λRA λRB = λ RA λFB = λFA

λRB = λFA λFB = λRA λFB = λRA

Note: FWHM denotes the full-width-at-half maximum bandwidth.

A temperature measurement experiment was conducted to evaluate the performance of the overlap spectrum FBG sensor based on light power demodulation. The experimental layout shown in Figure 4 comprised an ASE light source (Wavephotonics Co., Ltd., Hefei, China, model ASE-30-B; 3. Experiments and Discussion the wavelength covers the C-band; output power 30 mW), a four-port circulator (Shenjian A temperature Technology measurement wasChina), conducted to evaluate theOPMs performance Communication Co., experiment Ltd., Shenzhen, two cFBGs, and three (Shenzhenof the overlap spectrum FBG Co., sensor on light The experimental layout OSCOM Technology Ltd.,based Shenzhen, China,power model demodulation. XQ5210). The experimental configuration shown in Figure 4 could receive and transmitted light from theLtd., system. Although both shown in Figure 4 comprised an both ASEreflected light source (Wavephotonics Co., Hefei, China, model the reflection spectrumcovers and transmitted have the same aeffect for measurement as ASE-30-B; the wavelength the C-band;spectrum output power 30 mW), four-port circulator (Shenjian mentioned inTechnology theory, there is Ltd., a gapShenzhen, between theory andtwo reality. Therefore, the OPMs experimental Communication Co., China), cFBGs, and three (Shenzhen

OSCOM Technology Co., Ltd., Shenzhen, China, model XQ5210). The experimental configuration shown in Figure 4 could receive both reflected and transmitted light from the system. Although both the reflection spectrum and transmitted spectrum have the same effect for measurement as mentioned

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Sensorsthere 2018, 18, REVIEWtheory and reality. Therefore, the experimental configuration 6 of shown 10 in theory, is xaFOR gapPEER between in Figure 4 combined both configurations shown in Figure 1 and was designed to compare the configuration in REVIEW Figure 4 combined both configurations shown in Figure 1 and was designed Sensors 2018, 18, xshown FOR PEER 6 of 10 performance of the two configurations. to compare the performance of the two configurations.

configuration shown in Figure 4 combined both configurations shown in Figure 1 and was designed to compare the performance of the two configurations.

Figure 4. The configuration of a temperature test experiment. See text and Figure 1 for details.

Figure 4. The configuration of a temperature test experiment. See text and Figure 1 for details.

TheFigure spectrum the ASE source is shown intest Figure 5. It shows that theFigure flatness the spectrum 4. Theof configuration of a temperature experiment. See text and 1 forofdetails. was spectrum less than 1 of dBthe from 1537.5 nm to The reflection spectrum theflatness cFBGs should be in The ASE source is 1562.5 shownnm. in Figure 5. It shows thatof the of the spectrum this range to reduce the nonlinearity of the sensor system. cFBG A was fixed at a constant The spectrum of the ASE source is shown in Figure 5. It shows that the flatness of the spectrum was less than 1 dB from 1537.5 nm to 1562.5 nm. The reflection spectrum of the cFBGs should be in temperature °C), and1537.5 cFBGnm B of was placed insystem. a temperature-controlled (Ningbo Scientz was less than(15 1 dB from tothe 1562.5 nm. The reflection ofcabinet the should be in this range to reduce the nonlinearity sensor cFBG spectrum A was fixed at acFBGs constant temperature Biotechnology Co., Ltd., Ningbo, China, model DL-2020). The temperature was varied from −20 to this range to reduce the nonlinearity of the sensor system. cFBG A was fixed at a constant (15 ◦ C), and cFBG B was placed in a temperature-controlled cabinet (Ningbo Scientz Biotechnology Co., 100 °C. OPM A was connected to port 4 of the four-port circulator and received reflected light from temperature (15 °C), and cFBG B was placed in a temperature-controlled cabinet (Ningbo Scientz Ltd., Ningbo, China, model DL-2020). The temperature was varied from −20 to 100 ◦ C. OPM A was cFBG B. OPM BCo., wasLtd., connected to cFBG and received transmitted light from cFBG B. The accuracy Biotechnology Ningbo, China,Bmodel DL-2020). The temperature was varied from −20 to connected to port 4 of thecan four-port circulator and received reflected light from cFBG B. OPM B was of the measurements be severely affected by fluctuations of the intensity of the light source. 100 °C. OPM A was connected to port 4 of the four-port circulator and received reflected light from connected to OPM cFBG Bwas andconnected received from cFBG B. CThe measurements Therefore, theBtransmitted lighttotransmitted from received by OPM wasaccuracy usedcFBG to of monitor the light cFBG B. cFBGcFBG B andAlight received transmitted light from B.the The accuracy can be severely affected by fluctuations of the intensity of the light source. Therefore, the intensity fluctuations. If the light source fluctuated, the signal detected by OPM A and B were of the measurements can be severely affected by fluctuations of the intensity of the light transmitted source. light Therefore, from cFBG A received by OPM C was used to monitor the light intensity fluctuations. If the light divided by the the transmitted result received by from OPMcFBG C in order to suppress the influence of this effect. the light light A received by OPM C was used to monitor intensity fluctuations. If detected the light source fluctuated, the signal detected byresult OPMreceived A and Bby were source fluctuated, the signal by OPM A and B were divided by the OPM C -25 by divided by the result received in order to suppress the influence of this effect. in order to suppress the influence ofOPM this C effect.

Light Power (dbm) Light Power (dbm)

-25 -30

-30 -35

-35 -40

-40 -45

-45 -50

1530

1540 1550 Wavelength (nm)

1560

1570

-50

1530 1540 1550 1560 1570 (ASE) light source. Figure 5. The spectrum of a broadband-amplified spontaneous-emission Wavelength (nm)

TwoFigure groups of spectrum cFBGs were used in the experiment for comparison. Bothlight of source. their reflection 5. The a broadband-amplified spontaneous-emission (ASE) Figure 5. The spectrum of of a broadband-amplified spontaneous-emission (ASE) light source. bandwidths were 5 nm, and their reflection spectra were in the flat region of the ASE source. The cFBGs in the first of group were apodized, those in thefor second group were Their Two groups cFBGs were used inwhile the experiment comparison. Both unapodized. of their reflection Two groups oftransmission cFBGs were used in the experiment for of source. their reflection reflection and waveforms are spectra shown in Figure 6,flat andregion the detailed parameters are bandwidths were 5 nm, and their reflection were in thecomparison. of Both the ASE The bandwidths 52.nm, andwere their reflection spectra the flat region ofunapodized. the ASE source. shown in inwere Table cFBGs the first group apodized, while thosewere in theinsecond group were Their The cFBGs in the first were apodized, thoseininFigure the second were unapodized. reflection and group transmission waveforms while are shown 6, andgroup the detailed parameters areTheir shown in Table 2.

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reflection and transmission waveforms are shown in Figure 6, and the detailed parameters are shown Sensors 2018, in Table 2. 18, x FOR PEER REVIEW

7 of 10

-15

-10

cFBG A cFBG B Transmission spectra (dBm)

Reflection spectra (dBm)

-20

-25

-30

cFBG A cFBG B

-15 -20 -25 -30 -35

-35 -40

-40

1550

1552

1554 1556 Wavelength (nm)

-45 1550

1558

1552

1554 1556 Wavelength (nm)

(a)

1560

(b)

-40

-15

cFBG A cFBG B

cFBG A cFBG B

-20 Transmission spectra (dBm)

Reflection spectra (dBm)

1558

-45

-50

-25 -30 -35 -40 -45

-55 1546

1548

1550

1552 1554 Wavelength (nm)

1556

-50 1546

1558

1548

(c)

1550

1552 1554 Wavelength (nm)

1556

1558

(d)

280

50

1556

1554

45 275

slope=25 pm/°C

260

1554

255

250 -10

35

1553.5

30

slope=10 pm/°C

25 20 1553

15

0

20

40 60 Temperature (°C)

(e)

80

1553 100

10 -10

0

20

40 60 Temperature (°C)

80

100

(f)

Figure Figure 6. 6. Reflection Reflection spectra, spectra, transmission transmission spectra, spectra, and and temperature temperature characteristics characteristics of of chirp chirp FBGs FBGs (cFBGs) at a constant temperature (15 °C) for (a) reflection spectra of Group I; (b) transmission ◦ (cFBGs) at a constant temperature (15 C) for (a) reflection spectra of Group I; (b) transmission spectra spectra ofI;Group I; (c) reflection spectra II; (d) transmission II; (e) power reflected of Group (c) reflection spectra of GroupofII;Group (d) transmission spectra ofspectra Groupof II;Group (e) reflected vs. power vs. temperature, and center-wavelength vs. temperature for the cFBG B used in Group I; and temperature, and center-wavelength vs. temperature for the cFBG B used in Group I; and (f) reflected (f) reflected power vs. temperature, and center-wavelength vs. for temperature the in cFBG B used power vs. temperature, and center-wavelength vs. temperature the cFBG Bfor used Group II. in Group II.

Center-wavelength (nm)

265

Reflected power (μw)

1555

Center-wavelength (nm)

Reflected power (μw)

40 270

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Table 2. The detailed parameters of the cFBGs used in the experiment. Falling-Edge Wavelength (nm)

FWHM (nm)

Temperature Sensitivity Coefficient (pm/◦ C)

1553.65 1552.19

1557.04 1555.35

3.39 3.16

10 25

1550.00 1550.50

1553.77 1555.73

3.77 5.23

10 10

Rising-Edge Center-Wavelength Wavelength ◦ (nm, 15 C) (nm)

Group

Identifier

I

A B

1555.34 1553.67

II

A B

1551.37 1553.09

Figure 6e presents two relationship curves of the cFBG B of Group I. One is relationship between reflected power and temperature, and the other is center-wavelength vs. temperature. It shows that the reflectivity of cFBG B did not vary with temperature significantly. The slope of the center-wavelength vs. temperature curve is the temperature sensitivity coefficient of cFBG B. Figure 6f shows similar information for the cFBG B of Group II. Obviously, Group I corresponds to the situation in Figure 3c, while Group II corresponds to the situation in Figure 3b. According to Table 1 and Equation (9), the maximum theoretical measurement range of the sensor system was approximately 126 ◦ C for Group I and 377 ◦ C for Group II. The reflection waveform of Group I could be shifted 1.69 nm towards the long wave direction and 1.7 nm towards the short wave direction. This meant that the measurement range for Group I was from 73 ◦ C (15 ◦ C increasing by 58 ◦ C) to −53 ◦ C (15 ◦ C decreasing by 68 ◦ C). Similarly, the theoretical measurement range of Group II was from 342 ◦ C (15 ◦ C increasing by 327 ◦ C) to −35 ◦ C (15 ◦ C decreasing by 50 ◦ C). The experimental results were recorded at 5 ◦ C intervals and after 20 min, before the temperature reached the set value to uniformly heat the FBG. The relationship between the reflected (transmitted) power and the temperature is shown in Figure 7. Figure 7a–c shows the experimental results for Group I, and Figure 7d–f shows the results for Group II. Figure 7a,d indicates that the light source used in the experiment was fairly stable. Some interesting phenomena and results can be observed in Figure 7. First, the relationship curves between power and temperature for Group I were more smooth and linear when compared to the results for Group II. This was because the cFBGs in Group I were apodized. Their reflection spectra were therefore smooth, and the sidelobes were reduced. Second, Figure 7b,c shows that the relationships between the power of the light and temperature for Group I can be divided into two parts: a linear region and a saturation region. The turning point was at 75 ◦ C. The relationship curves had good linearity and the steep slope was in the linear region. However, the slope became flat in the saturation region, as the overlap spectrum had a maximum in the saturation region as shown in Figure 3c. Therefore, this temperature was beyond the measurement range of the system for Group I. According to the analysis of the measurement range, the upper limit of the system for Group I was 15 ◦ C increasing by 58 ◦ C. Thus, the upper limit was 73 ◦ C. This was in exact agreement with the experimental results. The curves in Figure 7e,f did not indicate a significant variation of the slope as the measurement range of the system in the case of Group II was large. The temperature range in the experiment did not extend beyond the measurement range. Finally, although using both the reflection spectrum for measurement and using the transmitted spectrum for measurement had the same performance in theory, the experimental results revealed different phenomena. The sensitivity when using the reflection spectrum in Group I was 0.034 µw/◦ C, and −0.054 µw/◦ C when using the transmitted spectrum. In Group II, the sensitivity was −0.578 nw/◦ C when using the reflection spectrum, and 0.425 nw/◦ C when using the transmitted spectrum. Furthermore, the linearity of the reflected power vs. temperature curve was better than that of the transmitted power vs. temperature curve. For example, the non-linear error of the linear region in Figure 7b was ~1.75%, and ~7.77% in Figure 7c. Similarly, the non-linear error was ~10.84% for Figure 7e and ~14.75% for Figure 7f. An important reason for the difference is that the reflection spectrum of FBG was not a perfect rectangular distribution and there were some sidelobes in the

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reflection of FBG. The Sensors 2018, spectrum 18, x FOR PEER REVIEW

overlap reflection spectrum from cFBG B reduced more sidelobes 9 of 10 than the transmitted spectrum because it was reflected twice by cFBG A and cFBG B. Therefore, a sensor system usingsystem reflected light from cFBG is expected than a system using Therefore, a sensor using reflected lightBfrom cFBG Btoisperform expectedbetter to perform better than a transmitted system usinglight. transmitted light. 70

5 4.5

75 °C

4 Transmitted power (μw)

Transmitted power (μw)

68

Measured results Linear fit

66

64

3.5

Linear region

Saturation region

3 2.5 2

62

1.5

60 -20

0.5 -20

1

0

20

40 60 Temperature (°C)

80

100

0

20

40 60 Temperature (°C)

(a)

80

100

(b) 133

6 Measured results Linear fit

5

132

Transmitted power (μw)

3 2

Saturation region

1 Linear region 0

Transmitted power (μw)

131 4

130 129 128 127 126 125

75 °C

-1 -2 -20

124 0

20

40 60 Temperature (°C)

80

123 -20

100

0

20

40 60 Temperature (°C)

(c)

(d) Measured results Linear fit

0.29

0.39 Transmitted power (μw)

0.28 Transmitted power (μw)

100

0.4

0.3

0.27 0.26 0.25 0.24

Measured results Linear fit

0.38 0.37 0.36 0.35 0.34

0.23 0.22 -20

80

0

20

40 60 Temperature (°C)

(e)

80

100

0.33 -20

0

20

40 60 Temperature (°C)

80

100

(f)

Figure Figure 7. 7. The The relationship relationship between between light light power power and and temperature temperature (a) (a) for for transmitted transmitted light light from from cFBG cFBG A in Group I, (b) for reflected light from cFBG B in Group I, (c) for transmitted light from A in Group I, (b) for reflected light from cFBG B in Group I, (c) for transmitted light from cFBG cFBG B B in in Group I, (d) for transmitted light from cFBG A in Group II, (e) for reflected light from cFBG B in Group I, (d) for transmitted light from cFBG A in Group II, (e) for reflected light from cFBG B in Group Group (f) for transmitted light fromB cFBG B inII. Group II. The line dashed line in the is fit a II, and II, (f) and for transmitted light from cFBG in Group The dashed in the figure is figure a linear linear fit using the least square method. using the least square method.

4. Conclusions In summary, an overlap spectrum FBG sensor based on light power demodulation was presented. The sensor used the overlap spectrum power of two cFBGs to detect changes in a measurand. Both the theoretical analysis and experimental results indicated that the relationship between the overlap spectrum power and the measurand exhibited good linearity. The experiment also revealed that FBG apodization and the configuration using reflected light could improve the performance of the sensor.

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4. Conclusions In summary, an overlap spectrum FBG sensor based on light power demodulation was presented. The sensor used the overlap spectrum power of two cFBGs to detect changes in a measurand. Both the theoretical analysis and experimental results indicated that the relationship between the overlap spectrum power and the measurand exhibited good linearity. The experiment also revealed that FBG apodization and the configuration using reflected light could improve the performance of the sensor. Author Contributions: H.Z. and J.J. contributed equally to this work. Conceptualization, H.Z. and J.J.; Data curation, S.L.; Formal analysis, X.Z. and H.C.; Investigation, J.J.; Project administration, H.Z.; Resources, H.C.; Supervision, Y.Q.; Writing, original draft, H.Z. Acknowledgments: This work was supported by the Natural Science Foundation of China (Grant No. 51607040), the Natural Science Foundation of Fujian Province of China (Grant No. 2016J01751), and the Smart Home Information Collection and Processing Internet of Things Laboratory of Digital Fujian. Conflicts of Interest: The authors declare no conflicts of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

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